DeWitt-Virasoro construction - High Energy Physics - Theory

Abstract: We study a particular approach for analyzing worldsheet conformal invariancefor bosonic string propagating in a curved background using hamiltonianformalism. We work in the Schrodinger picture of a single particle descriptionof the problem where the particle moves in an infinite-dimensional space.Background independence is maintained in this approach by adopting DeWitt-sPhys.Rev.85:653-661,1952 coordinate independent formulation of quantummechanics. This enables us to construct certain background independent notionof Virasoro generators, called DeWitt-Virasoro DWV generators, and invariantmatrix elements of an arbitrary operator constructed out of them in spin-zerorepresentation. We show that the DWV algebra is given by the Witt algebra withadditional anomalous terms that vanish for Ricci-flat backgrounds. The actualquantum Virasoro generators should be obtained by first introducing the vacuumstate and then normal ordering the DWV generators with respect to that. Wedemonstrate the procedure in the simple cases of flat and pp-wave backgrounds.This is a shorter version of arXiv:0912.3987 hep-th with many technicalderivations omitted.